Currently, I don't play on the PvP server as Blizzard is still working on their ruleset.

As it stands now, yes Undead and Humans can fight. Even on the PvE server. The only difference between servers, on the PvE server on group or the other has to go PvP. You can do this either by attacking a NPC or voluntarily. Then let the games begin!

Who would win? Depends on the players, not the races. :)

As it stands now, Undead do not have any major advantage over Humans, nor do Humans have any racial advantages over Undead. Undead is a great race to chose and play, but as mentioned above, Humans can be Paladins (the anti-undead class).